Add $ \, \color{blue}{ 3x^2-x+1 } \, $ and $ \, \color{orangered}{ 15-9x-2x^2 }$.

$$ \left( \color{blue}{3x^2-x+1} \right) + \left( \color{orangered}{15-9x-2x^2} \right) = x^2-10x+16 $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= 3x^2-x+1 \\ Q(x) &= -2x^2-9x+15 \\ \end{aligned} $$

Step 2: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrrr} & 3x^2 & -x & 1 \\ \color{blue}{ + } & -2x^2 & -9x & 15 \\ \hline \end{array} $$

Step 3: Combine like terms (add each column):

$$ \begin{array}{lrrr} & 3x^2 & -x & 1 \\ \color{blue}{ + } & -2x^2 & -9x & 15 \\ \hline & x^2 & -10x & 16 \end{array} $$

Polynomial Operations Calculator